Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2104.10623 · Physical Review A

rf-induced heating dynamics of noncrystallized trapped ions

Martin W. van Mourik, Pavel Hrmo, Lukas Gerster, Benjamin Wilhelm, R. Blatt, Philipp Schindler, Thomas Monz

Published Mar 7, 2022• 9 citations
arXivHTMLPDF

Abstract

We investigate the energy dynamics of noncrystallized (melted) ions, confined in a Paul trap. The nonperiodic Coulomb interaction experienced by melted ions forms a medium for nonconservative energy transfer from the radio-frequency (rf) field to the ions, a process known as rf heating. We study rf heating by analyzing numerical simulations of noncrystallized ion motion in Paul trap potentials, in which the energy of the ions' secular motion changes at discrete intervals, corresponding to ion-ion collisions. The analysis of these collisions is used as a basis to derive a simplified model of rf heating energy dynamics, from which we conclude that the rf heating rate is predominantly dependent on the rf field strength. We confirm the predictability of the model experimentally: Two trapped $^{40}\mathrm{Ca}^{+}$ ions are deterministically driven to melt, and their fluorescence rate is used to infer the ions' energy. Under these experimental conditions, we investigate which Doppler cooling parameters are required for efficient recrystallization, and compare our results to simulations.

DOI
10.1103/physreva.105.033101

Related papers

Dynamics of charged particles in a Paul radio-frequency quadrupole trap

John D. Prestage, Ann Katherine Williams, Lute Maleki +2 more

We have carried out a molecular-dynamics simulation of hundreds of ions confined in a Paul trap. The simulation includes the trapped particles' micromotion and interparticle Coulomb interactions. We have implemented a random walk in velocity to bring the secular motion to a given temperature which we have numerically measured. When the coupling \ensuremath{\Gamma} is large the ions form concentric shells which undergo a quadrupole oscillation at the rf frequency, while the ions within a shell form a 2D hexagonal lattice. Ion clouds at 5 mK show no rf heating for ${\mathit{q}}_{\mathit{z}}$\ensuremath{\lesssim}0.6, whereas rapid heating is seen for ${\mathit{q}}_{\mathit{z}}$=0.8.

Physical Review Letters•Jun 10, 1991•65 citations

Dynamics of Trapped Ions in the Presence of Laser Cooling and Radio-Frequency Heating

Yoshiharu Maeno Yoshiharu Maeno, Maki Tachikawa, Yoshiki Moriwaki +1 more

We establish a theoretical model which quantitatively describes the dynamics of laser cooled ions confined in a radio-frequency (rf) trap. In our model the laser cooling efficiency and the rate of collisional radio-frequency (rf) heating are explicitly formulated. Considering the balance between these two effects, the ion temperature is determined at each trap parameter. This model precisely reproduces the laser-induced-fluorescence (LIF) line profile observed for 24 Mg+ ions.

Japanese Journal of Applied Physics•Feb 1, 1995•14 citations

Far-from-equilibrium noise-heating and laser-cooling dynamics in radio-frequency Paul traps

Ananyo Maitra, Dietrich G. Leibfried, Denis Ullmo +1 more

We study the stochastic dynamics of a particle in a periodically driven potential. For atomic ions trapped in radio-frequency Paul traps, noise heating and laser cooling typically act slowly in comparison with the unperturbed motion. These stochastic processes can be accounted for in terms of a probability distribution defined over the action variables, which would otherwise be conserved within the regular regions of the Hamiltonian phase space. We present a semiclassical theory of low-saturation laser cooling applicable from the limit of low-amplitude motion to large-amplitude motion, accounting fully for the time-dependent and anharmonic trap. We employ our approach to a detailed study of the stochastic dynamics of a single ion, drawing general conclusions regarding the nonequilibrium dynamics of laser-cooled trapped ions. We predict a regime of anharmonic motion in which laser cooling becomes diffusive (i.e., it is equally likely to cool the ion as it is to heat it), and can also turn into effective heating. This implies that a high-energy ion could be easily lost from the trap despite being laser cooled; however, we find that this loss can be counteracted using a laser detuning much larger than Doppler detuning.

arXiv:1808.07816•Physical Review A•Apr 23, 2019•9 citations

Buffer gas cooling of ions in radio-frequency traps using ultracold atoms

Eleanor Trimby, Henrik Hirzler, Henning A. Fürst +3 more

Abstract Reaching ultracold temperatures within hybrid atom–ion systems is a major limiting factor for control and exploration of the atom–ion interaction in the quantum regime. In this work, we present results on numerical simulations of trapped ion buffer gas cooling using an ultracold atomic gas in a large number of experimentally realistic scenarios. We explore the suppression of micromotion-induced heating effects through optimization of trap parameters for various radio-frequency (rf) traps and rf driving schemes including linear and octupole traps, digital Paul traps, rotating traps and hybrid optical/rf traps. We find that very similar ion energies can be reached in all of them even when considering experimental imperfections that cause so-called excess micromotion. Moreover we look into a quantum description of the system and show that quantum mechanics cannot save the ion from micromotion-induced heating in an atom–ion collision. The results suggest that buffer gas cooling can be used to reach close to the ion’s groundstate of motion and is even competitive when compared to some sub-Doppler cooling techniques such as Sisyphus cooling. Thus, buffer gas cooling is a viable alternative for ions that are not amenable to laser cooling, a result that may be of interest for studies into cold controlled quantum chemistry and charged impurity physics.

arXiv:2109.15195•New Journal of Physics•Feb 22, 2022•15 citations

Motional heating of spatially extended ion crystals

Dimitri Kalincev, Laura S. Dreissen, A. P. Kulosa +3 more

We study heating of motional modes of a single ion and of extended ion crystals trapped in a linear radio frequency (rf) Paul trap with a precision of Δ ṅ ≈ 0.1 phonons s-1. Single-ion axial and radial heating rates are consistent and electric field noise has been stable over the course of four years. At a secular frequency of ω sec = 2π × 620 kHz, we measure ṅ = 0.56 (6) phonons s-1 per ion for the center-of-mass (com) mode of linear chains of up to 11 ions and observe no significant heating of the out-of-phase (oop) modes. By displacing the ions away from the nodal line, inducing excess micromotion, rf noise heats the com mode quadratically as a function of radial displacement r by phonons s-1 μm-2 per ion, while the oop modes are protected from rf-noise induced heating in linear chains. By changing the quality factor of the resonant rf circuit from Q = 542 to Q = 204, we observe an increase of rf noise by a factor of up to 3. We show that the rf-noise induced heating of motional modes of extended crystals also depends on the symmetry of the crystal and of the mode itself. As an example, we consider several 2D and 3D crystal configurations. Heating rates of up to 500 ph s-1 are observed for individual modes, giving rise to a total kinetic energy increase and thus a fractional time dilation shift of up to -0.3 × 10-18 s-1 of the total system. In addition, we detail how the excitation probability of the individual ions is reduced and decoherence is increased due to the Debye-Waller effect.

•Jan 1, 2021•12 citations

Chaos and order of laser-cooled ions in a Paul trap

R. Blümel, C. Kappler, W. Quint +1 more

We present recent experimental and theoretical results on the behavior of two-, three-, and four-ion crystals close to the Mathieu instability. In particular, we show that the crystals are stable until the Mathieu instability is reached, i.e., for the parameter space investigated, there is no ``melting'' of the crystals. Laser and rf heating are studied in detail. A simple model of chaotic rf heating as well as a classification of the ion dynamics into four characteristic regimes are presented.

Physical Review A•Jul 1, 1989•267 citations
We investigate the energy dynamics of noncrystallized (melted) ions, confined in a Paul trap. The nonperiodic Coulomb interaction experienced by melted ions forms a medium for nonconservative energy transfer from the radio-frequency (rf) field to the ions, a process known as rf heating. We study rf heating by analyzing numerical simulations of noncrystallized ion motion in Paul trap potentials, in which the energy of the ions' secular motion changes at discrete intervals, corresponding to ion-ion collisions. The analysis of these collisions is used as a basis to derive a simplified model of rf heating energy dynamics, from which we conclude that the rf heating rate is predominantly dependent on the rf field strength. We confirm the predictability of the model experimentally: Two trapped 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ions are deterministically driven to melt, and their fluorescence rate is used to infer the ions' energy. Under these experimental conditions, we investigate which Doppler cooling parameters are required for efficient recrystallization, and compare our results to simulations.
We have carried out a molecular-dynamics simulation of hundreds of ions confined in a Paul trap. The simulation includes the trapped particles' micromotion and interparticle Coulomb interactions. We have implemented a random walk in velocity to bring the secular motion to a given temperature which we have numerically measured. When the coupling \ensuremath{\Gamma} is large the ions form concentric shells which undergo a quadrupole oscillation at the rf frequency, while the ions within a shell form a 2D hexagonal lattice. Ion clouds at 5 mK show no rf heating for qz{\mathit{q}}_{\mathit{z}}qz​\ensuremath{\lesssim}0.6, whereas rapid heating is seen for qz{\mathit{q}}_{\mathit{z}}qz​=0.8.
We study the stochastic dynamics of a particle in a periodically driven potential. For atomic ions trapped in radio-frequency Paul traps, noise heating and laser cooling typically act slowly in comparison with the unperturbed motion. These stochastic processes can be accounted for in terms of a probability distribution defined over the action variables, which would otherwise be conserved within the regular regions of the Hamiltonian phase space. We present a semiclassical theory of low-saturation laser cooling applicable from the limit of low-amplitude motion to large-amplitude motion, accounting fully for the time-dependent and anharmonic trap. We employ our approach to a detailed study of the stochastic dynamics of a single ion, drawing general conclusions regarding the nonequilibrium dynamics of laser-cooled trapped ions. We predict a regime of anharmonic motion in which laser cooling becomes diffusive (i.e., it is equally likely to cool the ion as it is to heat it), and can also turn into effective heating. This implies that a high-energy ion could be easily lost from the trap despite being laser cooled; however, we find that this loss can be counteracted using a laser detuning much larger than Doppler detuning.
Abstract Reaching ultracold temperatures within hybrid atom–ion systems is a major limiting factor for control and exploration of the atom–ion interaction in the quantum regime. In this work, we present results on numerical simulations of trapped ion buffer gas cooling using an ultracold atomic gas in a large number of experimentally realistic scenarios. We explore the suppression of micromotion-induced heating effects through optimization of trap parameters for various radio-frequency (rf) traps and rf driving schemes including linear and octupole traps, digital Paul traps, rotating traps and hybrid optical/rf traps. We find that very similar ion energies can be reached in all of them even when considering experimental imperfections that cause so-called excess micromotion. Moreover we look into a quantum description of the system and show that quantum mechanics cannot save the ion from micromotion-induced heating in an atom–ion collision. The results suggest that buffer gas cooling can be used to reach close to the ion’s groundstate of motion and is even competitive when compared to some sub-Doppler cooling techniques such as Sisyphus cooling. Thus, buffer gas cooling is a viable alternative for ions that are not amenable to laser cooling, a result that may be of interest for studies into cold controlled quantum chemistry and charged impurity physics.
We study heating of motional modes of a single ion and of extended ion crystals trapped in a linear radio frequency (rf) Paul trap with a precision of Δ ṅ ≈ 0.1 phonons s-1. Single-ion axial and radial heating rates are consistent and electric field noise has been stable over the course of four years. At a secular frequency of ω sec = 2π × 620 kHz, we measure ṅ = 0.56 (6) phonons s-1 per ion for the center-of-mass (com) mode of linear chains of up to 11 ions and observe no significant heating of the out-of-phase (oop) modes. By displacing the ions away from the nodal line, inducing excess micromotion, rf noise heats the com mode quadratically as a function of radial displacement r by phonons s-1 μm-2 per ion, while the oop modes are protected from rf-noise induced heating in linear chains. By changing the quality factor of the resonant rf circuit from Q = 542 to Q = 204, we observe an increase of rf noise by a factor of up to 3. We show that the rf-noise induced heating of motional modes of extended crystals also depends on the symmetry of the crystal and of the mode itself. As an example, we consider several 2D and 3D crystal configurations. Heating rates of up to 500 ph s-1 are observed for individual modes, giving rise to a total kinetic energy increase and thus a fractional time dilation shift of up to -0.3 × 10-18 s-1 of the total system. In addition, we detail how the excitation probability of the individual ions is reduced and decoherence is increased due to the Debye-Waller effect.
We present recent experimental and theoretical results on the behavior of two-, three-, and four-ion crystals close to the Mathieu instability. In particular, we show that the crystals are stable until the Mathieu instability is reached, i.e., for the parameter space investigated, there is no ``melting'' of the crystals. Laser and rf heating are studied in detail. A simple model of chaotic rf heating as well as a classification of the ion dynamics into four characteristic regimes are presented.